I would say that as the group's size increases, the signal to noise ratio increases proportionally, until the only remaining viable path is authoritarian rule. (Otherwise, the apparatus of state is hamstrung by deadlock and petty dispute.)
This is why I do not desire "More people!". The best solution is not to continue "Growing!" eternally, but instead to assume a population size that is insufficient to measurably impact the actual literal health of the planet, despite the petty deadlock of its political apparati.
The alternative is Chinese Panopticon, times 9000.
To answer your specific queries-- within the contexts of those representational bodies-- the individual in a society of 150 individuals, is 1/150th of the vote within that power structure. If he or she is a very apt public speaker, they could indeed be very influential. Greek city-states were historically renown for this phenomenon, and produced fantastic orators for this very reason.
To be more specific-- that same person is 1/300millionth (ish), of the national vote. That is a reduction in effective agency of several orders of magnitude.
The fundamental problem arises when a social construct believes itself to be separate, and primal over its constituent components. When that happens, it becomes an authoritarian regime (since they only way for this to happen is to monopolize the use of force, and use it to coerce its components into compliance.). As stated, the typical reason this seems to happen is because of inability to reach agreement, as n-size of the body politik increases, and the odds of the "Cannot reach resolution" catastrophe increases, until probability equals 1.
Authoritarianism sidesteps this problem, by denying the foundation of that deadlock-- individual choice does not matter; Compliance is mandatory under threat of severe punishment, meted out by the authoritarian power structure.
The logically ideal scenario for humanity, is to accept that this is true about itself, and then make some decisions.
1) Decide to stop growing, and to voluntarily retract to a level that cannot inadvertantly destroy all life on the planet through such deadlock, and selfish individual agency.
2) Create a perfect authoritarian to run the planet.
3) Create a despot that can enforce either 1 or 2, before their regime implodes.
(and of course, 4-- Fail to do any of the above, and demonstrate why Fermi's paradox exists.)